It's down to either the LCD or the backlight in this case since everything else appears to be working. Turn out all the lights in the room and hold a flashlight up against the screen and see if you can make out an image.
If so, then the backlight has failed. It could be either a board issue or a display problem; I'm not familiar enough with the iPad to be able to tell you where the backlight driver circuits are and if they're repairable or not, but hopefully some of our experienced Apple technicians will know.
Otherwise if it's the backlight itself or the LCD, either way you'll have to replace the display, which won't be cheap.